No. You would set the origin so that it can be placed on the reference surface. I expect you would want to place the sink on the top so its lip sits down as the real one does.
Well, you should make a group or component of the counter top to keep it from sticking to other stuff. If you were to set up the component to cut an opening in the top, you would need to place the sink on the face inside the group or component. Keep in mind this opening is sort of an illusion. If you move the sink, the hole would move with it. If you remove the sink, the hole goes way, too. Not all that useful if your drawing is to be used for dimensioned drawings/plans. You might be better off to draw the top with the hole in it for the sink.
FWIW, as you make (or collect) components of a similar sort such as sinks, it would be a good idea to set their origins and axes in the same relative location. That makes it easy to swap one with another. In my work I wind up drawing a lot of case pieces with drawers and doors. Every knob or pull I create has the origin set in the same relative location so that I can not only place them in position without screwing around, I can also exchange them in an instant by selecting all of them and then right clicking on the new one in the Components window and choosing Replace Selected.